Main content

Applications of integration

AP Calc: CHA (BI), CHA‑4 (EU), CHA‑5 (EU), CHA‑6 (EU)
AP Calc: CHA (BI), CHA‑4 (EU), CHA‑4.B (LO), CHA‑4.B.1 (EK)
Learn
Average value over a closed intervalCalculating average value of function over intervalMean value theorem for integrals
Practice
Average value of a functionGet 3 of 4 questions to level up!
AP Calc: CHA (BI), CHA‑4 (EU), CHA‑4.C (LO), CHA‑4.C.1 (EK)
Learn
Motion problems with integrals: displacement vs. distanceAnalyzing motion problems: positionAnalyzing motion problems: total distance traveledMotion problems (with definite integrals)Worked example: motion problems (with definite integrals)Average acceleration over interval
Practice
Motion problems (with integrals)Get 3 of 4 questions to level up!
AP Calc: CHA (BI), CHA‑4 (EU), CHA‑4.D (LO), CHA‑4.D.1 (EK), CHA‑4.D.2 (EK), CHA‑4.E (LO), CHA‑4.E.1 (EK)
Learn
Area under rate function gives the net changeInterpreting definite integral as net changeWorked examples: interpreting definite integrals in contextAnalyzing problems involving definite integralsAnalyzing problems involving definite integralsWorked example: problem involving definite integral (algebraic)
AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.A (LO), CHA‑5.A.1 (EK)
Learn
Area between a curve and the x-axisArea between a curve and the x-axis: negative areaArea between curvesWorked example: area between curvesComposite area between curves
Practice
Area between a curve and the x-axisGet 3 of 4 questions to level up!
Area between two curves given end pointsGet 3 of 4 questions to level up!
Area between two curvesGet 3 of 4 questions to level up!
AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.A (LO), CHA‑5.A.2 (EK)
Learn
Area between a curve and the 𝘺-axisHorizontal area between curves
Practice
Horizontal areas between curvesGet 3 of 4 questions to level up!
AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.A (LO), CHA‑5.A.3 (EK)
Learn
No videos or articles available in this lesson
AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.B (LO), CHA‑5.B.1 (EK)
Learn
Volume with cross sections: introVolume with cross sections: squares and rectangles (no graph)Volume with cross sections perpendicular to y-axis
AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.B (LO), CHA‑5.B.2 (EK), CHA‑5.B.3 (EK)
Learn
Volume with cross sections: semicircleVolume with cross sections: triangle
AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.C (LO), CHA‑5.C.1 (EK)
Learn
Disc method around x-axisGeneralizing disc method around x-axisDisc method around y-axis
Practice
AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.C (LO), CHA‑5.C.2 (EK)
Learn
Disc method rotation around horizontal lineDisc method rotating around vertical lineCalculating integral disc around vertical line
Practice
Disc method: revolving around other axesGet 3 of 4 questions to level up!
AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.C (LO), CHA‑5.C.3 (EK)
Learn
Solid of revolution between two functions (leading up to the washer method)Generalizing the washer method
Practice
AP Calc: CHA (BI), CHA‑5 (EU), CHA‑5.C (LO), CHA‑5.C.4 (EK)
Learn
Washer method rotating around horizontal line (not x-axis), part 1Washer method rotating around horizontal line (not x-axis), part 2Washer method rotating around vertical line (not y-axis), part 1Washer method rotating around vertical line (not y-axis), part 2
Practice
AP Calc: CHA (BI), CHA‑6 (EU), CHA‑6.A (LO), CHA‑6.A.1 (EK)
Learn
Arc length introWorked example: arc length
Practice
Arc lengthGet 3 of 4 questions to level up!
AP Calc: CHA (BI), CHA‑4 (EU), CHA‑4.B (LO), CHA‑4.C (LO), CHA‑4.E (LO)
Learn
No videos or articles available in this lesson

About this unit

Definite integrals are all about the accumulation of quantities. Let's see how they are applied in order to solve various kinds of problems.
AP® is a registered trademark of the College Board, which has not reviewed this resource.